三角函数比值演示器

三角函数比值演示器
几何画板及绘图内容加载中,请稍等……
2017-09-15 11:10
①本范例演示根据用户输入的三角函数比值(正弦、余弦、正切等),动态绘制标准位置角对应的直角三角形及相关图形;②涉及核心数学概念包括三角函数定义、直角三角形边长关系、单位圆、坐标几何等;③作图要点运用了 GeoGebra 命令如 Denominator, Numerator, Intersect, Textfield, Dilate, Mirror, Segment, Angle, Distance, Polygon, SurdText 等,通过滑块和输入框实现用户交互;④适合高中数学教学,用于直观理解三角函数与几何图形的关联,提升空间想象能力。

GeoGebra 命令及参数

  1. Denominator(sine) → dsine
  2. Numerator(sine) → nsine
  3. Intersect(k_1, i) → B, C
  4. Textfield(cosine) → InputBox2
  5. Textfield(sine) → InputBox1
  6. Textfield(tangent) → InputBox3
  7. Textfield(PosSec) → InputBox6
  8. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], D) → A'
  9. Mirror(A', x = 0) → A''
  10. Segment(A, A') → l
  11. Segment(A, A'') → m
  12. Dilate(D, If[1 < j ≤ 2, 2 - j, 0], C) → D'
  13. Mirror(D', x = 0) → D''
  14. Segment(D, D') → n
  15. Segment(E, D'') → p
  16. Angle(C, D, A) → α
  17. Angle(A, E, B) → β
  18. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], C) → A'_1
  19. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], B) → A'_2
  20. Segment(A, A'_1) → q
  21. Segment(A, A'_2) → r
  22. Distance(D, C) → distanceDC
  23. Distance(A, C) → distanceAC
  24. Distance(A, B) → distanceAB
  25. Distance(E, B) → distanceEB
  26. Polygon(A, D, C) → poly1, c_1, a_1, d_1
  27. Polygon(A, B, E) → poly2, e_1, a_2, b_1
  28. Distance(D, C) → o
  29. Distance(E, B) → s
  30. Numerator(cosine) → ncosine
  31. Denominator(cosine) → dcosine
  32. Intersect(e, g) → F, G
  33. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], H) → A'_3
  34. Segment(A, A'_3) → f_1
  35. Dilate(H, If[1 < j ≤ 2, 2 - j, 0], F) → H'
  36. Segment(H, H') → g_1
  37. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], F) → A'_4
  38. Segment(A, A'_4) → h_1
  39. Polygon(A, H, F) → poly3, f_2, a_3, h_2
  40. Mirror(A, i_1) → A'_5
  41. Mirror(H, i_1) → H'_1
  42. Mirror(F, i_1) → F'
  43. Polygon(A'_5, H'_1, F') → poly3', f', a'_5, h'_1
  44. Mirror(H, i_1) → H'_2
  45. Mirror(H', i_1) → H''
  46. Segment(H'_2, H'') → j_1
  47. Mirror(A, i_1) → A'_6
  48. Mirror(A'_4, i_1) → I
  49. Segment(A'_6, I) → l_1
  50. Angle(F, H, A) → γ
  51. Angle(A, H, G) → δ
  52. Numerator(tangent) → ntangent
  53. Denominator(tangent) → dtangent
  54. Mirror(J, A) → J'
  55. Mirror(L, i_1) → L'
  56. Mirror(n_1, i_1) → q_1
  57. Angle(L, J, A) → ε
  58. Angle(A, J, N) → ζ
  59. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], J) → A'_7
  60. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], J') → A'_8
  61. Segment(A, A'_7) → r_1
  62. Segment(A, A'_8) → s_1
  63. Dilate(J, If[1 < j ≤ 2, 2 - j, 0], L) → J'_1
  64. Dilate(J, If[1 < j ≤ 2, 2 - j, 0], N) → J'_2
  65. Segment(J, J'_1) → t_1
  66. Segment(J, J'_2) → j_2
  67. Distance(J, J'_1) → distanceJJ'1
  68. Distance(J, J'_2) → distanceJJ'2
  69. Distance(A, A'_7) → distanceAA'7
  70. Distance(A'_8, A) → distanceA'8A
  71. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], L) → A'_9
  72. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], N) → A'_{12}
  73. Segment(A, A'_9) → k_2
  74. Segment(A, A'_{12}) → m_2
  75. Polygon(A, J, L) → poly4, l_3, a_4, j_3
  76. Polygon(A, J, N) → poly7, n_3, a_7, j_4
  77. Mirror(A, g_2) → A'_{10}
  78. Mirror(A'_9, g_2) → O
  79. Segment(A'_{10}, O) → l_2
  80. Mirror(A, r_1) → A'_{11}
  81. Mirror(A'_9, r_1) → P
  82. Segment(A'_{11}, P) → n_2
  83. Mirror(A'_{10}, s_1) → Q
  84. Mirror(O, s_1) → O'
  85. Segment(Q, O') → p_2
  86. Mirror(A, A) → A'_{13}
  87. Mirror(J, A) → J'_3
  88. Mirror(N, A) → N'
  89. Polygon(A'_{13}, J'_3, N') → poly7', n', a'_{13}, j'_3
  90. Mirror(J, A) → J'_4
  91. Mirror(J'_2, A) → R
  92. Segment(J'_4, R) → q_2
  93. Angle(A, J', K) → η
  94. Mirror(J, A) → J'_5
  95. Mirror(J'_1, A) → S
  96. Segment(J'_5, S) → r_2
  97. Mirror(A, A) → A'_{14}
  98. Mirror(J, A) → J'_6
  99. Mirror(L, A) → L'_1
  100. Polygon(A'_{14}, J'_6, L'_1) → poly4', l'_1, a'_{14}, j'_6
  101. Angle(M, J', A) → θ
  102. Distance(A, A'_3) → distanceAA'3
  103. Distance(D, D') → distanceDD'
  104. Distance(E, D'') → distanceED''
  105. SurdText(nsine / dsine) → text5
  106. SurdText(ncosine / dcosine) → text6
  107. SurdText(ntangent / dtangent) → text7
  108. Distance(J'_5, S) → distanceJ'5S

AI 绘图提示语参考

绘制一个基于给定正弦、余弦和正切值的三角函数动态演示图。首先输入正弦值,确定单位圆上的点A,然后根据正弦值在单位圆上找到点B和C。接着输入余弦值,通过相似三角形构造点D和D',并利用镜像和缩放操作得到点A'和A''。最后,通过距离和角度计算,绘制三角形和多边形,展示正弦、余弦和正切的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。